Best Known (70−64, 70, s)-Nets in Base 16
(70−64, 70, 65)-Net over F16 — Constructive and digital
Digital (6, 70, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
(70−64, 70, 238)-Net in Base 16 — Upper bound on s
There is no (6, 70, 239)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1670, 239, S16, 64), but
- the linear programming bound shows that M ≥ 279 042869 377374 270264 108023 819334 655299 764796 350225 244672 812708 637484 473502 509497 089627 662213 512335 337702 597977 925036 079329 247614 283496 292352 / 137 312738 338690 287152 519243 635363 888956 861415 239250 916437 > 1670 [i]